Results 21 to 30 of about 129 (51)
Almost commuting permutations are near commuting permutations [PDF]
, 2015 We prove that the commutator is stable in permutations endowed with the Hamming distance, that is, two permutations that almost commute are near two commuting permutations. Our result extends to $k$-tuples of almost commuting permutations, for any given $
Arzhantseva, Goulnara, Paunescu, Liviu
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Matrices that commute with their derivative. On a letter from Schur to Wielandt
, 2012 We examine when a matrix whose elements are differentiable functions in one variable commutes with its derivative. This problem was discussed in a letter from Issai Schur to Helmut Wielandt written in 1934, which we found in Wielandt's Nachlass.
Adkins +33 more
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The kernels of powers of linear operator via Weyr characteristic
, 2023 The adjoint of a matrix in the Lie algebra associated with a matrix algebra is a fundamental operator, which can be generalized to a more general operator $\varphi_{AB}: X\rightarrow AX-XB$ by two matrices $A$ and $B$.
Jian, Jie, Liao, Jun, Liu, Heguo
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On maximal distances in a commuting graph [PDF]
, 2010 We study maximal distances in the commuting graphs of matrix algebras defined over algebraically closed fields. In particular, we show that the maximal distance can be attained only between two nonderogatory matrices.
Dolinar, Gregor +2 more
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Sylvester matrix and common factors in polynomial matrices [PDF]
, 2007 With the coefficient matrices of the polynomial matrices replacing the scalar coefficients in the standard Sylvester matrix, common factors exist if and only if this (generalized) Sylvester matrix is singular and the coefficient matrices commute.
Wegge , Leon
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On the diameter of the commuting graph of the full matrix ring over the real numbers [PDF]
, 2017 In a recent paper C. Miguel proved that the diameter of the commuting graph of the matrix ring Mn(R) is equal to 4 if either n = 3 or n = 5. But the case n = 4 remained open, since the diameter could be 4 or 5.
Grau, J.M. +2 more
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Commuting Jordan Types: a Survey
, 2023 In this paper, we survey the progress in the problem of finding the maximum commuting nilpotent orbit that intersects the centralizer of a given nilpotent matrix.Comment: 17 Pages, 4 ...
Khatami, Leila
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One sided Star and Core orthogonality of matrices
, 2023 We investigate two one-sided orthogonalities of matrices, the first of which is left (right) $*$-orthogonality for rectangular matrices and the other is left (right) core-orthogonality of index $1$ matrices.
Ferreyra, D. E. +3 more
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On singular pencils with commuting coefficients [PDF]
We investigate the relation between the spectrum of matrix (or operator) polynomials and the Taylor spectrum of its coefficients. We prove that the matrix polynomial with commuting coefficients is singular, i.e.
Koval, Vadym, Pagacz, Patryk
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On approximate commutativity of spaces of matrices
, 2022 The maximal dimension of commutative subspaces of $M_n(\mathbb{C})$ is known. So is the structure of such a subspace when the maximal dimension is achieved.
Omladič, Matjaž +2 more
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